The choice of computational modeling technique can be based on a number of factors including: length scale, what variables are needed/relevant (e.g., time,
investigation of bonding characteristics requires the use of quantum mechanics and a very small length scale (nanometer) whereas thermal energy propagation in a nuclear reactor core may be on the order of meters and involve a continuum modeling approach. For this dissertation, the scope is narrowed to smaller length scales and methods that can be used to investigate electrical and phonon properties.
Equilibrium molecular dynamics (EMD) is one approach that can be used to calculate transport coefficients via the Green-Kubo formula (GKF).75,76 This is a widely
studied approach due to its ability to yield accurate thermal properties of large
materials;77-79 however, it does not account for electrical properties and is not well suited for 2D materials. For investigating the nanoscale regime, the use of density functional theory (DFT) is preferred because it incorporates electron density.
In this dissertation, the quantum mechanics-based method of DFT was employed to investigate these materials. Within DFT, there are a number of options for calculating transport properties of a material. Traditionally, DFT has been shown to underestimate bandgaps80 so many approaches have been proposed for improving band structure calculations. Among the more rigorous calculations include the use of hybrid
functionals81-84 which incorporate some exact exchange into the exchange correlation
interaction term and the GW approximation85 which involves the expansion of self- energies with respect to the single-particle Green’s function, G, and the screened Coulomb interaction, W. These calculations have the advantage of generating more accurate band structures without relying on empirical data; however, they greatly increase computational costs and are not easily suited for screening purposes. The semi-empirical method of DFT+U,86 which adds a Hubbard-like on-site Coulomb potential term to
account for strongly correlated electronic states, can be quickly and easily implemented to correct the overestimation and produce good quality band structures with negligible computational costs.
The calculation of thermal conductivity from first-principles is made possible through the full linearization of the Boltzmann transport equation for phonons.87 This is a very rigorous approach and involves the calculation of third-order force constants to account for phonon anharmonicity within the material. The computational costs are too high for screening purposes and it is not yet fully implemented for 2D materials;
however, second-order force constant calculations can account for normal processes with only moderate computational costs. The use of density functional perturbation theory (DFPT)88 allows for the calculation of necessary force constants and can produce phonon dispersion and density of states (DoS). This does not allow for the calculation of thermal conductivity but can provide useful phonon property information for materials screening.
This dissertation employs the use of DFT to screen structural, bonding, electrical, and phonon properties of 3D skutterudite and 2D TMD materials focusing on the effects of doping and heterostructures. The problem of understanding electrical and thermal transport in these materials is one of multiscale and multiphysics. There remains a lack of general knowledge that must be addressed through the use of large-scale materials
screening processes before more-rigorous calculations can be utilized. More information about the methods used in this work can be found in Chapter 3.
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CHAPTER THREE: MODELING ELECTRICAL AND THERMAL PROPERTIES IN THE SOLID STATE
The field of computational materials modeling is a fast growing area that offers a means of prediction and understanding beyond that of conventional research. By applying numerical models to emulate physical phenomena, we can analyze more wholly the